Optimality versus Practicality in Market Design: A Comparison of Two Double Auctions

We consider a market for indivisible items with m buyers, each of whom wishes to buy at most one item, and m sellers, each of whom has one item to sell. The traders privately know their values/costs, which are statistically dependent. Two mechanisms for trading are considered. The buyer's bid double auction collects bids and offers from traders and determines the allocation by selecting a market-clearing price. It fails to achieve all possible gains from trade because of strategic bidding by buyers. The designed mechanism is a revelation mechanism in which honest reporting of values/costs is incentive compatible and all gains from trade are achieved in equilibrium. This optimality, however, comes at the expense of plausibility: (i) the monetary transfers among the traders are defined in terms of the traders’ beliefs about each other's value/cost; (ii) a trader may suffer a loss ex post; (iii) the mechanism may run a surplus/deficit ex post. We compare the virtues of the simple yet mildly inefficient buyer's bid double auction to the flawed yet perfectly efficient designed mechanism.